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of 38
pro vyhledávání: '"Müyesser, Alp"'
A seminal result of Koml\'os, S\'ark\"ozy, and Szemer\'edi states that any n-vertex graph G with minimum degree at least (1/2 + {\alpha})n contains every n-vertex tree T of bounded degree. Recently, Pham, Sah, Sawhney, and Simkin extended this result
Externí odkaz:
http://arxiv.org/abs/2409.06640
An $\ell$-lift of a graph $G$ is any graph obtained by replacing every vertex of $G$ with an independent set of size $\ell$, and connecting every pair of two such independent sets that correspond to an edge in $G$ by a matching of size $\ell$. Graph
Externí odkaz:
http://arxiv.org/abs/2407.10565
We show that a $k$-uniform hypergraph on $n$ vertices has a spanning subgraph homeomorphic to the $(k - 1)$-dimensional sphere provided that $H$ has no isolated vertices and each set of $k - 1$ vertices supported by an edge is contained in at least $
Externí odkaz:
http://arxiv.org/abs/2407.06275
We show that the edges of any $d$-regular graph can be almost decomposed into paths of length roughly $d$, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$-regular graph
Externí odkaz:
http://arxiv.org/abs/2406.02514
We show that $(n,d,\lambda)$-graphs with $\lambda=O(d/\log^3 n)$ are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due to Han and Yang of the form $\lambda=d/\exp{(O(\sqrt{\log n
Externí odkaz:
http://arxiv.org/abs/2311.03185
Publikováno v:
Journal of Combinatorial Theory, Series B, Volume 169, November 2024, Pages 507-541
Let $G$ and $H$ be hypergraphs on $n$ vertices, and suppose $H$ has large enough minimum degree to necessarily contain a copy of $G$ as a subgraph. We give a general method to randomly embed $G$ into $H$ with good "spread". More precisely, for a wide
Externí odkaz:
http://arxiv.org/abs/2308.08535
Autor:
Müyesser, Alp
An orthomorphism of a finite group $G$ is a bijection $\phi\colon G\to G$ such that $g\mapsto g^{-1}\phi(g)$ is also a bijection. In 1981, Friedlander, Gordon, and Tannenbaum conjectured that when $G$ is abelian, for any $k\geq 2$ dividing $|G|-1$, t
Externí odkaz:
http://arxiv.org/abs/2303.16157
We study multigraphs whose edge-sets are the union of three perfect matchings, $M_1$, $M_2$, and $M_3$. Given such a graph $G$ and any $a_1,a_2,a_3\in \mathbb{N}$ with $a_1+a_2+a_3\leq n-2$, we show there exists a matching $M$ of $G$ with $|M\cap M_i
Externí odkaz:
http://arxiv.org/abs/2212.03100
Given a collection of hypergraphs $\textbf{H}=(H_1,\ldots,H_m)$ with the same vertex set, an $m$-edge graph $F\subset \cup_{i\in [m]}H_i$ is a transversal if there is a bijection $\phi:E(F)\to [m]$ such that $e\in E(H_{\phi(e)})$ for each $e\in E(F)$
Externí odkaz:
http://arxiv.org/abs/2209.09289
Autor:
Kamčev, Nina, Müyesser, Alp
Which patterns must a two-colouring of $K_n$ contain if each vertex has at least $\varepsilon n$ red and $\varepsilon n$ blue neighbours? In this paper, we investigate this question and its multicolour variant. For instance, we show that any such gra
Externí odkaz:
http://arxiv.org/abs/2209.06807